Question

Answer for question no. 10

Answer 1

Answer:

100 degrees

Step-by-step explanation:

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Answer 2

Answer:

Question :-

Angle ATO = 40°,find AOB

How to solve this sum?

→ First use all the information provided in the question

we need to prove the OT as bisector of Angle AOB by this way we will get the value of each angles.

Required Answer :-

Solution :-

OA perpendicular to AT - (given)

OB perpendicular to BT - (given)

Therefore,

Angle OAT = 90° -(i)

Angle OBT = 90° (ii)

In ∆ OAT and ∆ OBT,

1) OA congruent to OB

-(radius of same circle)

2) Angle OAT = Angle OBT = 90°

- (From i and ii)

3) AT congruent to BT

-(Tangent drawn from exterior point of

the circle are congruent)

4) therefore,

∆ OAT is congruent to ∆ OBT by SAS test of congruency.

5) OT congruent to OT -(c.s.c.t)

Therefore OT is the bisector of AOB.

In ∆ AOT,

Angle A + Angle O + Angle T = 180

90 + Angle O + 40 = 180

Angle O = 180 - 130

Angle O = 50°

Therefore Angle OBT will be 50° since ∆ OAT is congruent to ∆ OBT.

Angle OAT + Angle OBT = Angle AOB

-(Angle addition property)

50 + 50 = Angle AOB

Angle AOB = 100°

Final answer :-

Angle AOB = 100°

Hope it help you :)

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